SADC2-Exam2

What is static attitude determination?

It determines a spacecraft’s orientation by comparing measured vector directions with their known directions in the inertial frame.

What do attitude sensors measure?

hey measure direction, not distance or magnitude.
Example: a Sun sensor measures the direction toward the Sun.

What is the basic vector relationship?

v_KB=DCM_FBV_KF

The measured vector in the body frame equals the inertial-frame vector rotated into the body frame.

Why are at least two vector measurements needed?

Each unit vector provides only two independent equations. Attitude has three unknowns, so at least two nonparallel measurements are needed. This causes there to be 4 equations and 3 unknowns 4>3 = over determinate

Why is attitude determination really attitude estimation?

With two or more vector measurements, there are usually more equations than unknowns. The best attitude is estimated by minimizing measurement error. (error also occurs due to noise).

What does the q-method minimize?

J=0.5*sum[w_Kabs(v_KB-DCM_FBv_KF)]

It minimizes the weighted difference between measured and predicted vectors.

What do the weights w_K represent?

They indicate how trustworthy each measurement is. A more reliable sensor receives a larger weight.

What is the key result of the q-method?

K*q=lambda*q

The optimal quaternion q is the eigenvector associated with the largest eigenvalue of the 4×4 matrix(K)

Why is the largest eigenvalue used?

The cost function becomes

g=-lambda

Therefore, maximizing lambda minimizes the attitude error.

What are the main intermediate matrices in the q-method?

The measurements are used to form:

• B :weighted correlation matrix

• S=B+B^T :symmetric part of B

• sigma=trace(B)

• Z: vector containing the antisymmetric terms of B

• K: the final 4×4 matrix used in the eigenvalue problem

How does QUEST differ from the q-method?

The q-method solves the eigenvalue problem directly. QUEST approximates the largest eigenvalue as:

lambda_max=sum(w_K)

This avoids a full eigenvalue solution and is computationally faster.

What are Gibbs-Rodrigues parameters in QUEST?

They are an intermediate attitude representation:

p=q_vector/q4

Once p is found, it can be converted back into a unit quaternion.

What does ESOQ2 do differently from QUEST?

ESOQ2 also begins with the q-method, but it solves for Euler parameters and uses all four rows of the matrix \(K\). This can make it slightly more accurate or efficient than QUEST.

What is the main comparison between the three methods?

Method	Main idea
q-method	Solve the full eigenvalue/eigenvector problem
QUEST	Approximate the largest eigenvalue and solve a smaller system
ESOQ2	Use Euler parameters and all four equations for an efficient solution

q-method = exact eigenvector
QUEST = quick approximation
ESOQ2 = efficient Euler-parameter solution